Engineering - Rotational dynamics

Question 1

Definition of Inertia

Answer 1

A mass’ resistance to a change in velocity when subjected to a force

Question 2

Larger inertia of mass =

Answer 2

larger force required to change its velocity by a certain amount

Question 3

Definition of moment of inertia

Answer 3

a measure of an objects resistance to being rotationally accelerated about an axis

Question 4

Equation for the moment of inertia of a point mass

Answer 4

I = mr^+

Question 5

Equation for the moment of inertia of a point mass

Answer 5

I = mr^2

Question 6

What does ‘r’ stand for in the equation :
I = mr^2

Answer 6

The distance from the axis of rotation

Question 7

What is an object made up of more than one point mass called?

Answer 7

An extended object

Question 8

Equation of the moment of inertia of an object made up of more than one point mass (extended object)

Answer 8

I = ∑mr^2

Question 9

Factors affecting an object’s moment of intertia

Answer 9

-The object’s total mass
-How its mass is distributed about the axis of rotation, which varies as the distance from the axis of rotation ‘r’ is varied

Question 10

Equation to find the new moment of inertia ‘Inew’

Answer 10

Inew = I +mr^2

Question 11

Total KE of an object

Answer 11

The sum of the KEs of all the individual particles making up the objects

Question 12

Equation for KE linking moment of Inertia, I, and angular speed, ω.

Answer 12

1/2Iω^2

Question 13

Angular displacement

Answer 13

-θ
-angle through in any given direction in radians

Question 14

Angular speed

Answer 14

-ω
-angle an object moves through per unit time (only has magnitude)
-measured in rads^-1

Question 15

Angular velocity

Answer 15

-ω
-angle an object moves through per unit time (has magnitude and direction, clockwise or anticlockwise)
-measured in rads^-1

Question 16

Angular acceleration

Answer 16

-⍺
-change in angular velocity over time taken
-measured in rads^-2

Question 17

angular velocity =

Answer 17

angular displacement / time

Question 18

angular acceleration

Answer 18

angular velocity / time

Question 19

What does the area of an angular acceleration -time graph show?

Answer 19

The angular velocity

Question 20

What does the area of an angular velocity-time graph show?

Answer 20

The angular displacement

Question 21

What is torque?

Answer 21

The product of a force and its distance from the axis of rotation, in units Nm

Question 22

What are the equations for torque? (two)

Answer 22

-T = Fr
-T = I⍺

Question 23

What does the law of conservation of angular momentum state?

Answer 23

That when no external torque acts, the angular momentum of the system stats constant.

Question 24

Equation for conservation of momentum?

Answer 24

I1ω1 + I2ω2 = (I1 +I2)ω

Question 25

What is angular impulse?

Answer 25

The product of torque and its duration, where the applied torque is constant, and is equal to the change in angular momentum.

Question 26

Angular Impulse =

Answer 26

TΔt = Δ(Iω)

Question 27

How do you find the change in angular momentum from a Torque-time graph?

Answer 27

You find the area under the curve

Question 28

What is work done?

Answer 28

The force causing the motion multiplied by the distance travelled

Question 29

Work done =

Answer 29

Tθ

Question 30

What must work done overcome to increase the rotational kinetic energy of an object?

Answer 30

The friction torque

Question 31

How do you calculate the friction torque experimentally?

Answer 31

1. Apply an accelerating torque to the wheel to bring it up to a certain velocity
2. Remove the accelerating torque and measure the time taken for the wheel to come to rest
3. Calculate average deceleration using :
   ⍺ = (ω2 - ω1) / t
4. Calculate frictional torque using T = I⍺
   ( assuming that the moment of inertia is known)

Question 32

How do you work out work done from a Torque-angular displacement graph?

Answer 32

The area under the curve